Question: $\dfrac{d}{dx}[\cos(x)-7x]=$
Explanation: The expression to differentiate includes $\cos(x)$. Remember that the derivative of $\cos(x)$ is $-\sin(x)$. Put another way, $\dfrac{d}{dx}[\cos(x)]=-\sin(x)$. $\begin{aligned} &\phantom{=}\dfrac{d}{dx}[\cos(x)-7x] \\\\ &=\dfrac{d}{dx}[\cos(x)]-7\dfrac{d}{dx}(x) \\\\ &=-\sin(x)-7\cdot1 \\\\ &=-\sin(x)-7 \end{aligned}$ In conclusion, $\dfrac{d}{dx}[\cos(x)-7x]=-\sin(x)-7$